Comment on “Complete solution to a conjecture on Randić index”

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• 作者：Ljiljana Pavlovi&#x107
• 关键词：Graph theory ; Conjecture on Randi&#x107 ; index ; Quadratic programming model ; Linear programming ; Errors in proof
• 刊名：European Journal of Operational Research
• 出版年：2010
• 出版时间：16 November 2010
• 年：2010
• 卷：207
• 期：1
• 页码：539-542
• 全文大小：176 K

文摘

In this paper we will show that the proof of Theorem 2.1 from “Complete solution to a conjecture on Randić index”, by Xueliang Li, Bolian Liu and Jianxi Liu, European Journal of Operational Research 200, Issue 1, (2010), 9–13, is not correct. They tried to prove the conjecture given by M. Aouchiche, P. Hansen in “On a conjecture about the Randić index” (Discrete Mathematics, 307 (2), 2007, 262–265), but they failed in it. The mathematical model given by them is a problem of quadratic programming which they tried to solve by wrong use of linear programming. This error invalidates all further work.